ok, so if it's really a plesk issue, please excuse my bug report.
I only wonder, because the \r comes from 
$contents->getHeader(IMP_Contents::HEADER_TEXT)
and also there is no problem when forwarding emails.

Then this is a Plesk issue.

In our released versions of IMP, we have this in imp/lib/Compose.php:

                 $header_text = 
trim($resent_headers->toString(array('encode' => 'UTF-8'))) . "\n" . 
trim($contents->getHeader(IMP_Contents::HEADER_TEXT));

So if "\r\n" exists in that line, it has been inserted downstream.

Horde 5.1.4 was installed by Plesk update to 11.5

I found a solution for my problem by removing \r from $header_text in 
imp/lib/Compose.php. With only \n in $header_text i get \r\n in the 
Header which is correct. With \r\n it becomes \r\n\r\n in the received 
email header.

Can't reproduce.  You are using SMTP to send, right?

if you redirect an email, there is an empty line after each line of 
the original email header, so the email client is not able to display 
the email correctly.